Robustness surfaces of complex networks.

Area of Science:

• Network Science
• Complex Systems Analysis
• Data Science

Background:

• Complex network robustness is extensively studied, but a unifying framework for diverse metrics is lacking.
• Existing research faces challenges in dimensioning and weighting multiple robustness metrics for summation.
• There is a need for a standardized method to assess and compare network robustness across different scenarios.

Purpose of the Study:

• To propose a unifying framework for complex network robustness assessment.
• To introduce the R*-value and the concept of robustness surface (Ω) to address existing gaps.
• To enable effective comparison of robustness across different networks and failure scenarios.

Main Methods:

• Utilized Principal Component Analysis (PCA) as the core analytical tool.
• Normalized initial network robustness to 1.
• Identified the most informative robustness metric for specific failure scenarios and percentages.
• Constructed the robustness surface (Ω) by aggregating metric values across various failure conditions.

Main Results:

• Demonstrated that networks exhibit distinct robustness surfaces (dissimilar shapes) based on failure scenarios and metric sets.
• The robustness surface effectively visualizes network robustness variability.
• The proposed framework facilitates direct comparison of robustness between different networks.

Conclusions:

• The R*-value and robustness surface provide a unified approach to quantifying complex network robustness.
• This framework overcomes limitations in dimensioning and weighting multiple robustness metrics.
• The robustness surface offers a powerful tool for network analysis, comparison, and understanding resilience under various threats.